>> mhelp csgn
csgn - sign function for real and complex expressions
Calling Sequence
csgn(x)
csgn(1, x)
csgn(0, x, y)
Parameters
x - any algebraic expression
y - any algebraic expression
Description
- The csgn function is used to determine in which half-plane ("left" or "right")
the complex-valued expression or number x lies. It is defined by
/ 1 if Re(x) > 0 or Re(x) = 0 and Im(x) > 0
csgn(x) = <
\ -1 if Re(x) < 0 or Re(x) = 0 and Im(x) < 0
- The value of csgn(0) is controlled by the environment variable _Envsignum0.
The 3-argument calling sequence csgn(0, x, y) sets _Envsignum0 = y for the
duration of the call to csgn. See signum for further information.
- The decision of whether or not to perform many of the automatic symmetry
transformations in maple is based on the value of csgn. For example, if
csgn(x) = -1, the transformation sin(x) --> -sin(-x) is done.
- csgn uses signum to determine the signs of Re(x) and Im(x).
- The derivative of csgn is denoted by csgn(1, x). This is 0 for all
non-purely-imaginary numbers, and is undefined otherwise.
- For mathematical consistency, the value of csgn(0), as determined either by
the value of _Envsignum0 or by the third argument to csgn, should be either 0
(the default) or one of 1, -1, or undefined.
Examples
> csgn(1-2/3*I);
1
> csgn(exp(2*Pi/3*I));
-1
> csgn(Pi);
1
> diff(csgn(x), x);
csgn(1, x)
> csgn(1,-3+I);
0
See Also
evalc, sign, signum, inifcns, assume